On the tail of the waiting time in a Markov-modulated M/G/1 queue

Sören Asmussen and Colm Art O'Cinneide

Department of Mathematical Statistics,
Lund Institute of Technology,
Lund University,
1998

ISSN 0281-1944
ISRN LUNFD6/NFMS--3200--SE


Abstract:
We show that the "exponential decay parameter" of the waiting time in a Markov-modulated M/G/1 queue is no larger than that of the corresponding M/G/1 queue with "averaged" parameters, and we give a stringent necessary and sufficient condition for equality. We also explore the effect of speeding up the modulation process. A key tool is a Markov-modulated fluid model.